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I have a doubt , please help me out !!

In the given figure , P , Q , R are 3 complex numbers . Angle PQR = \(\theta\)

How do I represent theta using only the amplitudes of the given complex numbers ?

Also if \(Z_1 Z_2 Z_3\) be 3 complex numbers taken in the complex plane in the anticlockwise sense , then how can I represent the angle \(Z_1 Z_2 Z_3\) in terms of the individual amplitudes of the complex numbers ?

P.S. The angles/amplitude part of the complex numbers is the only thing that has kept me confused , the other parts ar clear to me . Please help me out !!

Note by Uchiha Robert
2 years, 1 month ago

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I'm assuming that by amplitudes you mean magnitudes. I don't know if there is an equation exclusively in terms of the magnitudes, but this link discusses the dot product adapted for complex vectors, from which you can determine \(\theta.\) Brian Charlesworth · 2 years, 1 month ago

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@Brian Charlesworth Thanks for the link sir . But I was referring to the angle made by the complex number with the origin sir as in argument of a complex number .

I am not able to understand the concept of arg \(\frac{Z_1 - Z_2}{Z_3-Z_2}\) , what does it mean and how to use it in calculations ? This is my doubt sir , please see the pic that I have provided sir ? Uchiha Robert · 2 years, 1 month ago

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